Speckle with non-Rayleigh amplitude distribution has significant research value in imaging and measurement using structured illumination. However, existing speckle customizing schemes have been limited in generation speed due to the refresh rate of spatial light modulators (SLMs). In this work, we proposed a method to rapidly generate non-Rayleigh distributed speckle fields using a digital micro-mirror device (DMD). In contrast to SLMs that allow for gray-scale phase modulation, DMD is limited to binary amplitude control. To solve this limitation, we design a Gerchberg-Saxton-like algorithm based on super-pixel method, this algorithm enables the customization of non-Rayleigh speckle with arbitrary intensity probability density function. Statistical analyses of experimental results have demonstrated that the customized speckles exhibit excellent stability in their lateral statistical properties, while also maintaining consistent propagation characteristics with Rayleigh speckle in the longitudinal direction. This method provides a new approach for high-speed and arbitrary intensity speckle customization, holding potential applications in imaging, measurement, and encryption fields.